Actually, even if posted, you can still carry in the bar. This goes for any property or business that is not on the list of places you can't carry in, i.e.: government/federal buildings, courthouses, schools, etc.

"No Guns" signs in Colorado do not carry the "Force of Law". Reference.

HOWEVER... if someone at the property suspects you of carrying, or accidentally sees you carrying (or I guess if they just want to be a dick and don't know about your gun at all), they can ask you to leave, and you must comply.